A device of thus kind is known from DE-U 2 97 04 759. With this known arrangement, the sharpening tool is formed as a rectangular bar. The bar may be turned. However, the effective working length is limited to a comparatively small central area, since the bar must be held reliably. Therefore, the available effective working length is comparatively quickly worn out. Therewith, a comparatively short total tool life and therewith a comparatively bad material exploitation and altogether a bad economic efficiency results.